Silicon Photonics: Fundamentals and Devices

7.6 Modulation Bandwidth under Injection

Since the linear and quadratic EO effects in silicon are not significant, in most of the studies of modulation the injection of carriers is accepted as the most effective means of introducing RI change in the material. The structures actually used will be discussed in detail in Section 7. For the present context, it is sufficient to note that injection or carrier removal from a region of silicon material is accomplished by using a biased p–n or, rather, a p–i–n diode. Application of a forward bias injects electrons and holes into the depletion layer in the p–n diode or into the intrinsic (i) layer in the p–i–n diode. The modulation speed of the device depends on the recombination lifetime of the electron–hole pairs as may be understood by the following analysis 1.

The carrier lifetime τ is defined such that it represents the total recombination time of charged carriers in the absence of stimulated recombination. It is defined by the relation

(7.20)

where n is the carrier density, and R_r and R_nr denote, respectively, the radiative and nonradiative recombination rates.

To find out the modulation response, one needs to set up a rate equation for carriers. Since electrons and holes are injected in pairs and also recombine in pairs, it is enough to consider one type of carrier. The rate equation should include all the mechanisms by which carriers ...